In the Wheatstone bridge diagram below, resistor R 1 is a Nichrome type V strain

Question

In the Wheatstone bridge diagram below, resistor R1 is a Nichrome type V strain gage with nominal resistance of 100 ? at 25

In the Wheatstone bridge diagram below, resistor R1 is a Nichrome type V strain gage with nominal resistance of 100 ? at 25 degree C, a gage factor of 2.0, and a temperature coefficient of 400 ppm/ degree C. The gage is bonded on the surface to a beam in order to measure axial strain during loading. The remaining ballast resistors in the bridge have a fixed resistance of 100 ?, and the excitation voltage is 5.0 V.

Explanation / Answer

The bridge is in equilibrium when
R1*R4 =R3*R2

Em = U/(R1+R2) *R1 - U/(R3+R4)*R3

The only component value that varies is R1. We differentiate the above relation and get

d(Em) = U/(R1+R2) *dR1

d(Em)/U = dR1/(R1+R2)

dR1 = (R1+R2)*d(Em)/U = (100+100)*0.00235/5 =0.094 ohm

dR1/R1 = 0.094/100 =9.4*10^-4 =940 ppm

the gage factor is

G = (dR1/R1) / (dL/L)

strain =(dL/L) = (dR1/R1) /G = 940/2 =470 ppm

Second case (increasing temeparture)

dR1/R1 = dT*alpha = (40-25)*400*10^-6 =6*10^-3

dR1 = 6*10^-3*100 =0.6 ohm

d(Em) = dR1/(R1+R2) *U =0.6/200 *5 =0.015 V =15 mV

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